Okay, so these aren't the "best", or even my favorite games, but I like them. These flash games are all free and while you won't be able to split the atom after playing them, they should help develop your problem solving skills. The geography flash game is the only game here where you will acquire knowledge instead of skills.

Light-Bot is a fun introduction to programming. Create commands for your robot and then watch him (or her?) test them out.

3D Logic helps you think more 3 dimensionally. Connect three sides of a cube together by color. Gets challenging towards the end.

Splitter 2 is a fun game with basic problem solving physics. Mostly ball and levers.

Red Remover is more of a kids game, but still fun for adults (I have no idea what the Russian broadcast played at the end means). Manipulate blocks and balls.

Factory Balls 2 is imaginative and fun. Build balls in a factory. Hint on level 19: If you water a seed 3 times the flowers disappear.

Geography flash games. Test your knowledge of geography of the world. Includes United States, Europe, Middle East, Central America, South America, Africa, Canada, and Australia.

If interested, also check out these business-minded free market games.